@Rodal or anyone for that matter know how to calculate shawyer's design factor?

Shawyer's Df equation is attached. Have verified with Shawyer that it is correct.

Writing x0,x1,x2 for the 3 lambdas, this can be expressed as D = [(1-a)/sqrt(a)] * [sqrt(b)/(1-b)], where a = x1/x2, b = x02/(x1*x2)Notice that D is a separable function of a,b and so can be readily optimised by inspection.Dmax -> infinity when a->0 and/or b->1.Do other relations between x0,1,2 exist to prevent D becoming infinite?Obviously if a > 0 and b < 1 then Dmax when a is min, b is max

I would like to know the maximum theoretical value of Df.Based on the expression I derived above, it corresponds to - a min, i.e. (x1/x2) min- b max, i.e. x02/(x1*x2) max.

What are the values of aMin and bMax, and why?

I stopped looking at the Design Factor as a serious formula as soon as I learnt from TheTraveller that it uses the "cut-off" frequency for an open waveguide of constant cross-section, as it is known that tapered waveguides and cavities do NOT have rigid cut-off. Only constant cross-section waveguides have a rigid cut-off condition.

Which are not a problem for the well-funded Chinese [..] Space Program.

What makes you think it's well funded? Last I heard, the best estimates put it below ESA.. i.e., about a third of the US program.

What makes you think it's not well funded? After all, it's claimed to be a revolutionary propulsion paradigm. The chief reason that would occur to most people is that it's not funded because it doesn't actually work. I wonder if there'll be a paper about that.

Suppose it does work and they don't publicize it because its such a revolutionary advancement that gives them a major advantage on the final frontier....

@Rodal or anyone for that matter know how to calculate shawyer's design factor?

Shawyer's Df equation is attached. Have verified with Shawyer that it is correct.

Writing x0,x1,x2 for the 3 lambdas, this can be expressed as D = [(1-a)/sqrt(a)] * [sqrt(b)/(1-b)], where a = x1/x2, b = x02/(x1*x2)Notice that D is a separable function of a,b and so can be readily optimised by inspection.Dmax -> infinity when a->0 and/or b->1.Do other relations between x0,1,2 exist to prevent D becoming infinite?Obviously if a > 0 and b < 1 then Dmax when a is min, b is max

I would like to know the maximum theoretical value of Df.Based on the expression I derived above, it corresponds to - a min, i.e. (x1/x2) min- b max, i.e. x02/(x1*x2) max.

What are the values of aMin and bMax, and why?

I stopped looking at the Design Factor as a serious formula as soon as I learnt from TheTraveller that it uses the "cut-off" frequency for an open waveguide of constant cross-section, as it is known that tapered waveguides and cavities do NOT have rigid cut-off. Only constant cross-section waveguides have a rigid cut-off condition.

Fair enough. So what formula (if any) can you recommend for calculation of the thrust-to-power ratio?

@Rodal or anyone for that matter know how to calculate shawyer's design factor?

Shawyer's Df equation is attached. Have verified with Shawyer that it is correct.

Writing x0,x1,x2 for the 3 lambdas, this can be expressed as D = [(1-a)/sqrt(a)] * [sqrt(b)/(1-b)], where a = x1/x2, b = x02/(x1*x2)Notice that D is a separable function of a,b and so can be readily optimised by inspection.Dmax -> infinity when a->0 and/or b->1.Do other relations between x0,1,2 exist to prevent D becoming infinite?Obviously if a > 0 and b < 1 then Dmax when a is min, b is max

I would like to know the maximum theoretical value of Df.Based on the expression I derived above, it corresponds to - a min, i.e. (x1/x2) min- b max, i.e. x02/(x1*x2) max.

What are the values of aMin and bMax, and why?

I stopped looking at the Design Factor as a serious formula as soon as I learnt from TheTraveller that it uses the "cut-off" frequency for an open waveguide of constant cross-section, as it is known that tapered waveguides and cavities do NOT have rigid cut-off. Only constant cross-section waveguides have a rigid cut-off condition.

Fair enough. So what formula (if any) can you recommend for calculation of the thrust-to-power ratio?

The one of Dr. Notsosureofit, a formula by a Ph.D. in Physics, knowledgeable of General Relativity and Radar, and a formula that is explicitly dependent on the mode shape:

Which are not a problem for the well-funded Chinese [..] Space Program.

What makes you think it's well funded? Last I heard, the best estimates put it below ESA.. i.e., about a third of the US program.

What makes you think it's not well funded? After all, it's claimed to be a revolutionary propulsion paradigm. The chief reason that would occur to most people is that it's not funded because it doesn't actually work. I wonder if there'll be a paper about that.

Suppose it does work and they don't publicize it because its such a revolutionary advancement that gives them a major advantage on the final frontier....

Good find...hey, the good news is its observable but not explainable. If it does get explained through unusual measurement error, that benefits folks. If it gets explained thru new physics...well, you know the rest

...You may want to put more effort into calculating whether these effects can account for the forces observed (micro-newtons) or conducting something similar to the experiment I described for detecting these particles.

Again, I hope I'm wrong! It would be great to see an analyses that says "Yes, these effects are occurring but they cannot account for the thrust because of X."

Outgassing and electrical corona breakdown discussion in the thread go back to very early in early threads, by different individuals. Bringing up multipaction is something that we appreciate your bringing up to the thread. SeeShells has specifically thought about these effects in her design. Rfmwguy also has a perforated shell to reduce most gas effects.

SeeShells ( http://www.gofundme.com/yy7yz3k) has a comprehensive program to look at the effects you are describing including a camera to film what's happening inside the EM Drive through her perforated EM Drive.

What additional efforts, specifically, would you suggest that SeeShells has not taken to examine the effects you are describing ?

So if you or one of your friends within that 50 mile radius want to put a couple bucks to help not to make more millions but because they choose to dream, I'll welcome it.

Shell

*grin* I put a little into your fund the day you started it. Like I said, I want to believe. I'll have a lot more faith in your data (once you have it) than random unsubstantiated statements.

That just made my day, thank you. It's been kind of hectic since my mom passed but I got a little time today and tomorrow. I've scheduled the whole day in the shop/Lab. She would have wanted nothing less.

Unfortunately this is far from the level of details we have from Eagleworks (from "anomalous thrust..." + a lot from Paul March as answers here on NSF). If any one finds more information about this balance please link.

At least an explanation exists for why the Chinese don't already have production lines for churning out EmDrives. Can there be any other excuse?

Lack of power at ground level. Lack of millions of potential buyers. Translation; lack of market.

Which are not a problem for the well-funded Chinese Air Force and Space Program. Lack of a market has not impeded their on-going Taikonaut and Mini-Space Station programs, Space Defense tests, as well as their long-term programs including ion-drives and Moon program. So, why no deployment of the Yang EM Drive in Space, if it can really do what is claimed?

I would expect they are looking for more thrust and truthfully we don't know the politics around it. Yang could have said I can get you more thrust for more time and funds (you know the types:) ) or it could have been a a bust. We simply don't know and that's the bottom line. Because we simply don't know we should still run through the tests.

The device used by Tajmar looks more like a version of Shawyer's first fustrum than the latest work by Yang, et al. It would be very nice if we could get actual schematics of Tajmar's fustrum rather than squinting at pictures trying to figure out what he did...

<clip>So if you or one of your friends within that 50 mile radius want to put a couple bucks to help not to make more millions but because they choose to dream, I'll welcome it.

Shell

I am game. Maybe you can get a kickstarter togetger. I would contribute and I am sure more people would too

It's at the bottom of my post under Crazy Eddie is getting a little more crazy.

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes TMmnp and TEmnp, for suitable m and n values.

Evidently p=1 is best, which is what I would expect (for example: TE011 is better than TE012 which is better than TE013). Similarly TE111 is better than TE112 which is better than TE113. Ditto for TM modes: TM111 is better than TM112 which is better than TM113. Because lower modes have greater amplitude.

Outside of Notsosureofit's formula there is the question of whether having a stronger field near the apex is better or worse. Inspection of the Wolfram/Mathematica analysis of Meep runs reveals this story which to me is becoming more clear.

...You may want to put more effort into calculating whether these effects can account for the forces observed (micro-newtons) or conducting something similar to the experiment I described for detecting these particles.

Again, I hope I'm wrong! It would be great to see an analyses that says "Yes, these effects are occurring but they cannot account for the thrust because of X."

Outgassing and electrical corona breakdown discussion in the thread go back to very early in early threads, by different individuals. Bringing up multipaction is something that we appreciate your bringing up to the thread. SeeShells has specifically thought about these effects in her design. Rfmwguy also has a perforated shell to reduce most gas effects.

SeeShells ( http://www.gofundme.com/yy7yz3k) has a comprehensive program to look at the effects you are describing including a camera to film what's happening inside the EM Drive through her perforated EM Drive.

What additional efforts, specifically, would you suggest that SeeShells has not taken to examine the effects you are describing ?

Good to hear there was a discussion, although I couldn't find one when searching the forum - hence why I decided to post my initial thoughts in May. Perhaps I was searching using different terminology. Where could I find it? I'm particularly curious about how they have been discounted.

And is there more detail somewhere as to how SeeShells has taken these effects into account? The primary test I would run would be the test under vacuum I suggested in the post linked above which includes a few RF checks (like observing return loss). For that I would add a coupler in order to observe return loss vs. input power. A camera is nice but a disassembly and inspection under a microscope is more conclusive. Regardless, the new paper referenced above did find visual evidence of these effects so I will assume they are relatively common among the EMDrives that have been built. So I would proceed assuming you will find evidence of these effects either from the camera or visual inspection. Also, I'm not entirely sure if a camera would detect these effects. Particularly the newest paper shows thrust after RF power is removed indicating to me that localized heating is generating the propellent which wouldn't be visible necessarily. Perhaps you mean a thermal imaging camera like that used in the paper which would be better.

Not sure a perforated design would help either as particle generation even on a flat plate will generate some minute force.. just how minute is the question.

-JK

I've repasted the details of the vacuum test below:

"Hi Everyone,

Just checking in and reading through some comments. Thanks for taking a look at the potential forces involved, rgreen. I believe a force from atomized particles on the interior could have similar - or stronger - effect than being generated on the exterior even if your design is properly vented in vacuum. Especially if the cavity was not designed to be hermetic but is not intentionally vented. Think of a balloon with a pin-hole in it. I did some searching and couldn't find the word "hermetic" or "vented" in the paper or discussions but perhaps the design is vented. If it is designed to be hermetic I would suggest publishing the results of a fine and gross leak test as a hermetic design of this size with braised glass seals for the launch is non-trivial. With a small leak you could have built a simple thruster. The sensitivity of that leak test would need to be appropriate to catch a particle stream that equates to millionths-of-a-pound (more tangible units than "micronewtons" to me) of thrust. This effect could occur in our out of vacuum. This is all speculation and hand-waving though as I don't know all the details of your assembly. While I can't say the exact mechanism that would cause a force to occur, I think it is possible this force is present (sound familiar? ).

Regardless, putting on my "NASA Independent Reviewer" hat, I would say that if you are claiming to have developed a technology which can provide propulsion without a propellant, you have a burden of proof to show that you are not self-generating your propellant due to RF energy interacting with the materials in your setup. These materials could include your metals, coatings, adhesives, dielectrics and / or contaminants. I don't believe there is sufficient evidence from the test points over a range of power levels and in and out of vacuum and across test teams (US, China, Britain) to confirm or refute this as I can imagine situations where particle generating effects would occur in any case due to out-gassing, breakdown, corona, multipaction etc. I am not involved in your effort at all so please forgive my intrusion but from an RF engineering perspective it would be great to see a paragraph in a paper someday explaining how you tested for these effects and can now dismiss them and that you havn't inadvertently built a conventional thruster or ion drive. I saw an earlier post suggesting a wiki be developed which would include potential sources of error and this topic could be filed there.

I believe a good test would involve at least following (again, my apologies if these were done in part or seem obvious.. I am also repeating myself a bit here from earlier posts):

1 - Add sufficient vent holes to the RF cavity. Ensure the hole diameter is small enough such that their wave-guide effects do not effect the S11 of the system in the range you're operating in. It seems you do have an ability to do 3D e-mag simulations but here is a tool you can use to verify the venting does not have a significant electrical impact: http://multipactor.esa.int/features.html. Unless you have specifically designed the system to be hermetic with glass seals etc, it will slowly leak and confuse the test and possibly be the source of thrust. Hopefully you are not currently relying on your antenna launch or fasteners on the cavity caps for venting. Testing under vacuum is actually the best way to resolve this issue and is the "relevant space environment" (i.e. high TRL!) so hermetic designs should be avoided as this helps your case anyways. The proposed physics don't require a gas to be present, correct? To be clear, whether or not you are currently vented does not confirm or refute anything as I can envision scenarios where a force would be generated even with a properly vented design in normal atmosphere from the momentum imparted by the particles at the focused atomization point (millionths-of-a-pound!)... so this is just a first step.

2 - Ensure you perform an un-powered elevated temperature bake-out of the DUT and support electronics at 50 to 60C for least 24 hours under vacuum. This is generally what we do for RF space-flight hardware as that is what is required to get most of the typical volatiles out of a system. It looks like this was done for the chamber but the DUT does not appear to have been heated. This needs to include any support electronics - in fact, move all but the bare minimum of electronics outside the chamber. Completion of most out-gassing should be observed not with your vacuum pump monitor but with a TQCM in real-time (http://en.wikipedia.org/wiki/Quartz_crystal_microbalance). Note- this bake-out is a pretty crucial step to eliminate the possibility of simple out-gassing being the culprit for this phenomenon. Out-gassing can be a non-linear behavior in some materials. Some materials out-gas at a rate proportional to their temperature. Others will not begin out-gassing until they reach a certain temperature. So the experimenter should perform an un-powered bake-out over the range of temperatures the *powered* system should expect to see. So if you are dissipating 2.6W in your cavity a thermal analysis should be done to see what temperature the system (especially the launch) would get to in vacuum. Alternatively just instrument it properly and run a test first. A bake-out will need to be properly done prior to every test as re-exposure to atmosphere will re-coat the DUT with contaminants and your dielectric will absorb moisture. A mistake we made on the Aquarius mission (http://aquarius.nasa.gov/) was not performing a high temperature bake-out with our heaters once we reached orbit. Consequently it took weeks for the system to stabilize as the dielectrics out-gassed moisture and we could observe the dielectric constant of RF boards drifting. In short, ensure the un-powered temperatures reach and exceed the temperatures caused by RF heating when operational at the test temperature.

[General note on the 2.6W case as it is often used for an argument against the causes I have listed: Some have noted the 2.6W test is "low" but that is a huge amount of power for parts to handle in my field (RF radiometry). For example, consider that few of the passive parts sold by these folks can handle more than a watt or 10s of watts unless they are specially engineered for high power applications: http://www.minicircuits.com/ Consider what is actually occuring in the part when you reach the maximum power level and could that effect generate enough particles to create millionths-of-a-pound of pressure. Also, in many components the limiting factor is the launch design. Returning to your test setup, your PTFE insert will certainly heat and out-gas due due to a portion of the 2.6W of RF power being dissipated within it. I note the slow time-constant on the plot in Figure 22 looks an awful lot like what you would see from a thermal effect, particularly as thrust slowly decays after RF power is removed: http://arc.aiaa.org/doi/pdf/10.2514/6.2014-4029. Also I interpret the setup as 2.6W being dissipated in chamber but with 28W incident from the power amps with the related electric field levels of 28W in your system. This is my understanding based on this statement in Part B of http://arc.aiaa.org/doi/pdf/10.2514/6.2014-4029: " In this test configuration, the VNA system indicated a quality factor of ~7320, and the difference of power forward and power reflected as reported by the power meters was indicated to be ~16.92 watts as a result of manual tuning to maximize the power difference. " So for purposes of thermal effects, 2.6W is correct. But for breakdown effects, the electric field strength associated with 28W is what should be considered, simulated and evaluated against breakdown.]

3 - Once the system is stabilized, I would turn on the RF power transmitting into an RF coaxial short rather than a load, perhaps with an RF switch. A full reflection which is a worst-case in your system could cause issues on your source and induce some out-gassing or breakdown from that device. Ensure the TQCM does not detect anything. This will let you know if your setup would cause a false-negative for the test I'm proposing. Generally, ensure you have brought on an experienced materials or contamination engineer to set this test up for you. Also this would serve as further proof there are not a conducted or radiated interference issue. The paper notes the DC currents from the power amps do effect the measurement to a degree so this case is more similar to what the amps are actually driving just to be thorough.

4 - Turn on your system in the normal test setup and observe the TQCM. If particles are detected you may have found the culprit as these may be the result of out-gassing, breakdown, corona, multipaction, etc. These effects all generate particles and correspond to different power levels and environments. This step can be tricky but I've seen it work well when experienced people are involved. When you have pulled a vacuum, small particle generation detection is more reliant on Brownian motion etc. to cause particles to exit the vent holes and get to the detector so some care is required here. As I mentioned in an earlier comment this was the method used to verify that multipaction was occuring within the SMAP diplexers and not a purely reactive effect.

5- Allow the system to run for at least a week to ensure the force does not dissipate or change due to a propellant being expended. Also, if possible, increase the sampling rate of your force sensor to be faster than what one would see from thermal effects. I'm not at all familiar with the proposed physics to explain the phenomenon but generally a purely RF cause should result in "instantaneous" force. Faster than milliseconds should be enough to discount thermal effects although not all the sources of error I have mentioned are thermal.

6 - (Mentioned this previously) - Open the cavity and have someone experienced inspect the materials for any evidence of breakdown. A detailed inspection and cleaning should be done before the unit is sealed if that is possible.

So hopefully some of this is helpful. Someone else may be able to devise a more compelling test for the hypothesis. In summary, there are a variety of particle generating effects of high RF power including out-gassing, corona breakdown, multipaction, plasmas, etc. Each can occur at different power levels, some will occur in vacuum, some not. It is possible each of the teams is seeing one or more of these effects depending on these variables during any given test. The above statements are general and also apply to the tests done by the Chinese and British teams and any future test. So while "multipaction" may not be the current culprit with the setup at 28W it could be as testing is done at higher power levels. I have focused much of the above discussion on the small 28W case in the referenced paper but KW of RF energy are known to cause somewhat violent events including (but not always) magic smoke and burned components. So generating a newton of force during these events seems conceivable.

I dug around online for resources related to high power breakdown at RF frequencies and couldn't find much. Here are a few things but these may a bit too basic.

I hope this post wasn't too rambling or too full of misconceptions regarding the tests you have performed. I don't envy you folks trying to make progress on this complex issue via a public internet forum. Good luck, and again, I hope I'm wrong!

Final note for any students here who are curious about RF: This is far below the power levels I believe you have operated at but for future consideration at the 100W to KW level note the acoustic (i.e. pressure) effects of this demonstration which uses a 2.4GHz magnetron in a closed cavity with a contaminant: Depending on the dynamics involved, teams which have tested at high power could be seeing the effects of a similar unstable vibration (think of your vibrating cell-phone skittering across the table.)"

@Rodal or anyone for that matter know how to calculate shawyer's design factor?

Shawyer's Df equation is attached. Have verified with Shawyer that it is correct.

Writing x0,x1,x2 for the 3 lambdas, this can be expressed as D = [(1-a)/sqrt(a)] * [sqrt(b)/(1-b)], where a = x1/x2, b = x02/(x1*x2)Notice that D is a separable function of a,b and so can be readily optimised by inspection.Dmax -> infinity when a->0 and/or b->1.Do other relations between x0,1,2 exist to prevent D becoming infinite?Obviously if a > 0 and b < 1 then Dmax when a is min, b is max

I would like to know the maximum theoretical value of Df.Based on the expression I derived above, it corresponds to - a min, i.e. (x1/x2) min- b max, i.e. x02/(x1*x2) max.

What are the values of aMin and bMax, and why?

I stopped looking at the Design Factor as a serious formula as soon as I learnt from TheTraveller that it uses the "cut-off" frequency for an open waveguide of constant cross-section, as it is known that tapered waveguides and cavities do NOT have rigid cut-off. Only constant cross-section waveguides have a rigid cut-off condition.

Fair enough. So what formula (if any) can you recommend for calculation of the thrust-to-power ratio?

The one of Dr. Notsosureofit, a formula by a Ph.D. in Physics, knowledgeable of General Relativity and Radar, and a formula that is explicitly dependent on the mode shape:

Thanks and I took a look at this. Taken at face value it predicts that, in order to maximise the thrust/power ratio, one requires that independently:- Ds/Db to be minimum- Db to be minimum- L to be minimumeven after accounting for the frequency scaling per Appendix I.The thrust predictions seem roughly in line with the experimental data.k = F/P seems to be, for the ranges graphed, about 3*10-7 N/W (about 300 uN for 1000 W).

I'm looking for a way to get much higher F/P values. I've indicated how this can be done per this formula.I would welcome some concrete suggestions.

[A couple of notes on this derivation:1. In Appendix I the n factor due to L is omitted (but the scaling conclusion is correct anyway)2. Whenever I read about "accelerated photons" my toes curl up]

Spaceflight. I've avoided useage of the term without enough ground test results, but it might be time to plant a seed of discussion for the future considering Tajmar's paper. We will need to think about electric power for a smallsat. That will not be easy.

A magnetron is not 100% efficient, meaning that this type of device would require north of 1kW of electric power. This is not easily attainable on a satellite. RTGs are usually much below this.:

Searching these threads in NSF with NSF supercalifragilisticexpialidocious search function is a non-starter, and using Google to search through 600 of these pages is something that I don't relish, so suffice it to say that Prof. Yang, who claims by far the greatest thrust forces and greatest thrust/InputPower ever claimed for an EM Drive is prominent for bringing up the presence of ions inside the cavity of the EM Drive as the means of propulsive force, in her peer-reviewed papers (although she does not elaborate as to why she brings up the ions inside the cavity ).

The reason why when opening the thread at periodic times you may not see these issues being discussed "du jour" is easy to explain:

1) Once brought up, and not being able to be eliminated, not much people can continue to discuss, as there are really no dissenting parties that are going to be arguing about it. However, discussions about conservation of energy and free-energy are continuously ongoing, as recent as an article just appeared in Wired with the headline about reaching Pluto in 18 months with an EM Drive...

2) Everybody is more fascinated to talk about "New Physics" than down to earth explanations. Talking about warping space will bring you big ratings. Corona discharge... not so much

3) Corona discharge, multipaction are not as easy to discuss and model mathematically as conservation of energy etc.

4) It is to the credit of experimenters like SeeShells and Rfmwguy and others that they have taken the bull by the horns, and they have decided to test using their own resources and time.

Thanks for the explanation on how to test about these effects, since I had forgotten you had written such a comprehensive testing program proposal

Spaceflight. I've avoided useage of the term without enough ground test results, but it might be time to plant a seed of discussion for the future considering Tajmar's paper. We will need to think about electric power for a smallsat. That will not be easy.

A magnetron is not 100% efficient, meaning that this type of device would require north of 1kW of electric power. This is not easily attainable on a satellite. RTGs are usually much below this.:

The three curves represent p=1, p=2 and p=3, where p is the quantum number in the longitudinal direction, for modes TMmnp and TEmnp, for suitable m and n values.

Evidently p=1 is best, which is what I would expect (for example: TE011 is better than TE012 which is better than TE013). Similarly TE111 is better than TE112 which is better than TE113. Ditto for TM modes: TM111 is better than TM112 which is better than TM113. Because lower modes have greater amplitude.

Outside of Notsosureofit's formula there is the question of whether having a stronger field near the apex is better or worse. Inspection of the Wolfram/Mathematica analysis of Meep runs reveals this story which to me is becoming more clear.

I'm shooting for TE112 first shot but meep is a little lacking using an antenna other than the placements. Have a few ideas other than just throwing the antenna in the cavity.

Wasn't aero going to try to excite a mode in the side wall with a snub center to top and bottom today with the itsybitsy cavity? It was also suggested that a square pad could be made simulating a loop that could excite a TE mode, wonder what happened to that line of thought?